Dynamic response of micro-pillar sensors measuring fluctuating wall-shear-stress

We present in this paper test results of flexible micro-pillars and pillar arrays for wall shear stress measurements in flows with fluctuating wall shear stress such as unsteady separated flows or turbulent flows. Previous papers reported on the sensing principle and fabrication process. Static calibrations have shown this sensor to have a maximum nonlinearity of 1% over two orders of wall-shear-stress. For measurements in flows with fluctuating wall shear stress the dynamic response has been experimentally verified in an oscillating pipe flow and compared to a calculated response based on Stokes’ and Oseen’s solution for unsteady flow around a cylinder. The results demonstrate good agreement under the given boundary conditions of cylindrical micro-pillars and the limit of viscous Stokes-flow around the pillar. Depending on the fluid and pillar geometry, different response curves result ranging from a flat low-pass filtered response to a strong resonant behavior. Two different methods are developed to detect the frequency content and the directional wall shear stress information from image processing of large sensor films with arrays of micro-pillars of different geometry. Design rules are given to achieve the optimal conditions with respect to signal-to-noise ratio, sensitivity and bandwidth for measurements in turbulent flows.     

Turbulence in rough-wall boundary layers: universality issues

Wind tunnel measurements of turbulent boundary layers over three-dimensional rough surfaces have been carried out to determine the critical roughness height beyond which the roughness affects the turbulence characteristics of the entire boundary layer. Experiments were performed on three types of surfaces, consisting of an urban type surface with square random height elements, a diamond-pattern wire mesh and a sand-paper type grit. The measurements were carried out over a momentum thickness Reynolds number (Re _θ) range of 1,300–28,000 using two-component Laser Doppler anemometry (LDA) and hot-wire anemometry (HWA). A wide range of the ratio of roughness element height h to boundary layer thickness δ was covered (0.04 ￡ h/d ￡ 0.400.04 \leq h/\delta \leq 0.40). The results confirm that the mean profiles for all the surfaces collapse well in velocity defect form up to surprisingly large values of h/δ, perhaps as large as 0.2, but with a somewhat larger outer layer wake strength than for smooth-wall flows, as previously found. At lower h/δ, at least up to 0.15, the Reynolds stresses for all surfaces show good agreement throughout the boundary layer, collapsing with smooth-wall results outside the near-wall region. With increasing h/δ, however, the turbulence above the near-wall region is gradually modified until the entire flow is affected. Quadrant analysis confirms that changes in the rough-wall boundary layers certainly exist but are confined to the near-wall region at low h/δ; for h/δ beyond about 0.2 the quadrant events show that the structural changes extend throughout much of the boundary layer. Taken together, the data suggest that above h/δ ≈ 0.15, the details of the roughness have a weak effect on how quickly (with rising h/δ) the turbulence structure in the outer flow ceases to conform to the classical boundary layer behaviour. The present results provide support for Townsend’s wall similarity hypothesis at low h/δ and also suggest that a single critical roughness height beyond which it fails does not exist. For fully rough flows, the data also confirm that mean flow and turbulence quantities are essentially independent of Re _θ; all the Reynolds stresses match those of smooth-wall flows at very high Re _θ. Nonetheless, there is a noticeable increase in stress contributions from strong sweep events in the near-wall region, even at quite low h/δ.     

The turbulence structure of drag-reduced boundary layer flow

The structure of turbulence in a drag-reduced flat-plate boundary layer flow has been studied with particle image velocimetry (PIV). Drag reduction was achieved by injection of a concentrated polymer solution through a spanwise slot along the test wall at a location upstream of the PIV measurement station. Planes of velocity were measured parallel to the wall (x–z plane), for a total of 30 planes across the thickness of the boundary layer. For increasing drag reduction, we found a significant modification of the near-wall structure of turbulence with a coarsening of the low-speed velocity streaks and a reduction in the number and strength of near-wall vortical structures.     

BOUNDARY TREATMENT AND AN EFFICIENT PRESSURE ALGORITHM FOR INTERNAL TURBULENT FLOWS USING THE PDF METHOD

The generalized Langevin model, which is used to model the motion of stochastic particles in the velocity–composition joint probability density function (PDF) method for reacting turbulent flows, has been extended to incorporate solid wall effects. Anisotropy of Reynolds stresses in the near-wall region has been addressed. Numerical experiments have been performed to demonstrate that the forces in the near-wall region of a turbulent flow cause the stochastic particles approachi ng a solid wall to reverse their direction of motion normal to the wall and thereby, leave the near-wall layer. This new boundary treatment has subsequently been implemented in a full-scale problem to prove its validity. The test problem considered here is that of an isothermal, non-reacting turbulent flow in a two-dimensional channel with plug inflow and a fixed back-pressure. An efficient pressure correction method, developed in the spirit of the PISO algorithm, has been implemented. The pressure correction strategy is easy to implement and is completely consistent with the time- marching scheme used for the solution of the Lagrangian momentum equations. The results show remarkable agreement with both k–ϵ and algebraic Reynolds stress model calculations for the primary velocity. The secondary flow velocity and the turbulent moments are in better agreement with the algebraic Reynolds stress model predictions than the k– ϵ predictions. © 1997 by John Wiley & Sons, Ltd.     

The nature of near-wall convection velocity in turbulent channel flow

A novel notion of turbulent structure the local cascade structure-is introduced to study the convection phenomenon in a turbulent channel flow. A space-time cross-correlation method is used to calculate the convection velocity. It is found that there are two characteristic convection speeds near the wall, one associated with small-scale streaks of a lower speed and another with streamwise vortices and hairpin vortices of a higher speed. The new concept of turbulent structure is powerful to illustrate the dominant role of coherent structures in the near-wall convection, and to reveal also the nature of the convection-the propagation of patterns of velocity fluctuations-which is scale-dependent.     

A general one-equation turbulence model for free shear and wall-bounded flows

The purpose of thiswork is to introduce a complete and general one-equation model capable of correctly predicting a wide class of fundamental turbulent flows like boundary layer, wake, jet, and vortical flows. The starting point is the mature and validated two-equation k−ω turbulence model of Wilcox. The newly derived one-equation model has several advantages and yields better predictions than the Spalart-Allmaras model for jet and vortical flows while retaining the same efficiency and quality of the results for near-wall turbulent flows without using a wall distance. The derivation and validation of the new model using findings computed by the Spalart-Allmaras and the k−ω models are presented and discussed for several free shear and wall-bounded flows.     

On the mechanism of turbulence suppression by spanwise surface oscillations

The attenuation of turbulent pulsations in near-wall flows by means of spanwise periodic surface oscillation is examined. A direct numerical simulation of the flow in a circular pipe with imposed rotational oscillations has shown that for Re=4000 and the optimal oscillation frequency, the degree of turbulence attenuation increases with increase in the oscillation amplitude until the flow relaminarizes. The estimated optimal frequency ω⁺=0.06. The results of applying the theory of the development of near-wall coherent structures agree qualitatively with those of numerical simulation. It is concluded that the intensity of the pulsations is reduced because the spanwise movements weaken the longitudinal vortices which cause turbulent bursts in near-wall flows. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 37–44, March–April, 2000. The research was carried out with financial support from the Russian Foundation for Basic Research (project No. 99-01-01095).     

On near-wall hot-wire measurements

A specially constructed hot-wire probe was used to obtain very near-wall velocity measurements in both a fully developed turbulent channel flow and flat plate boundary layer flow. The near-wall hot-wire probe, having been calibrated in a specially constructed laminar flow calibration rig, was used to measure the mean streamwise velocity profile, distributions of streamwise and spanwise intensities of turbulence and turbulence kinetic energy k in the viscous sublayer and beyond; these distributions compare very favorably with available DNS results obtained for channel flow. While low Reynolds number effects were clearly evident for the channel flow, these effects are much less distinct for the boundary layer flow. By assuming the dissipating range of eddy sizes to be statistically isotropic and the validity of Taylor's hypothesis, the dissipation rate ɛ _iso in the very near-wall viscous sublayer region and beyond was determined for both the channel and boundary layer flows. It was found that if the convective velocity U _c in Taylor's hypothesis was assumed to be equal to the mean velocity Uˉ at the point of measurement, the value of (ɛ⁺ _iso)₁ thus obtained agrees well with that of (ɛ ⁺)_DNS for y ⁺ ≥ 80 for channel flow; this suggests the validity of assuming U _c=Uˉ and local isotropy for large values of y ⁺. However, if U _c was assumed to be 10.6u _τ , the value of (ɛ⁺ _iso)₂ thus obtained was found to compare reasonably well with the distribution of (ɛ⁺ _iso)_DNS for y ⁺≤ 15. Received: 31 May 1999/Accepted: 20 December 1999     

Inducing 3D vortical flow patterns with 2D asymmetric actuation of artificial cilia for high-performance active micromixing

Driven by the advancement of the “lab-chip” concept, a new beating behavior of artificial cilia was identified to meet the demands on rapid and complete fluid mixing in miniaturized devices. This beating behavior is characterized by an in-plane asymmetric motion along a modified figure-of-eight trajectory. A typically symmetric figure-of-eight motion was also tested for comparison. Results showed that with this new beating behavior, the mixing efficiency for complete mixing is 1.34 times faster than that with the typical figure-of-eight motion. More importantly, the required beating area was only approximately two-thirds of that in the typical figure-of-eight motion, which is beneficial for more compact designs of various “lab-chip” applications. The unique planar asymmetric motion of the artificial cilia, which enhanced the magnitudes of the induced three-dimensional (3D) flow, was identified by micro-particle image velocimetry (µPIV) measurement and numerical modeling as a major contributor in enhancing microscale mixing efficiency. Quantitatively, 3D vortical flow structures induced by the artificial cilia were presented to elucidate the underlying interaction between the artificial cilia and the surrounding flow fields. With the presented quantification methods and mixing performance results, a new insight is provided by the hydrodynamic advantage of the presented micromixing concept on efficiently mixing highly viscous flow streams at microscale, to leverage the attributes of artificial cilia in the aspect of microscale flow manipulation.     

Large Eddy Simulation of the Flow Over a Three-Dimensional Hill

This paper investigates the use of LES for a flow around a three-dimensional axisymmetric hill. Two aspects of this simulation in particular are discussed here, the resolution and the inlet boundary conditions. In contrast to the LES of flows with sharp edge separations which do not require the near-wall dynamics to be fully resolved, the hill flow LES relies on the resolution of the upstream boundary layer in order to provoke the separation at a correct position. Although around 15 ×10⁶ computational cells were used, the resolution of streaky structures in the near-wall region that are important for a LES is not achieved. Two different inlet boundary conditions were used: the steady experimental profile and the time-dependent boundary conditions produced from DNS results of low Reynolds number channel flow. No significant improvement in the results was obtained with the unsteady inlet condition. This indicates that, although the unsteady inlet boundary conditions may be necessary for a successful LES of this flow, they must be followed with the resolution of the boundary layer for a successful LES.     

Active Control of a Circular Cylinder Flow at Transitional Reynolds Numbers

Active and passive control of flow around a circular cylinder, at transitional Reynolds numbers was investigated experimentally by measuring cylinder surface pressures and wake velocity profiles. Two- and three-dimensional passive boundary layer tripping was considered and periodic active control using piezo-fluidic actuators was introduced from a two-dimensional slot that was nearly tangential to the cylinder surface. The slot location was varied circumferentially by rotating the cylinder and this facilitated either upstream- or downstream-directed actuation using sinusoidal or modulated wave-forms. Separation was controlled by two distinct methods, namely: by forcing laminar-turbulent transition when applied at relatively small angles (30–60°) from the forward stagnation point; and by directly forcing the separated shear-layer at larger angles. In the latter case, actuation produced the largest load changes when it was introduced at approximately 90° from the forward stagnation point. When the forcing frequency was close to the natural vortex-shedding frequency, the two frequencies “locked-in” creating clear and persistent structures. These were examined and categorized. The “lock-in” effect lowered the base pressure and increased the form-drag whereas delaying separation from the cylinder did the opposite.     

A study in transitional flat plate boundary layers: measurement and visualization

 This study is concerned with transition in flat plate boundary layer flow. Sets of results are obtained as follows: (1) Very clear pictures of the formation and the development of the butterfly-like structures rather than ∧-structures in the K-regime of boundary layer transition are obtained. (2) A chain of ring like vortices, which generate the high-frequency spikes on the time traces of velocity and still present periodical behaviour, at the tip of each ∧-vortex, which is the part of the butterfly-like structure, are visualized for the first time. (3) A wave-like structure is observed to occupy the whole boundary layer, extending from the near-wall region to the outer edge of the boundary layer. Received: 24 September 1998/Accepted: 24 April 1999     

Three‐dimensional numerical simulation of red blood cell motion in Poiseuille flows

An immersed boundary method based on an FEM has been successfully combined with an elastic spring network model for simulating the dynamical behavior of a red blood cell (RBC) in Poiseuille flows. This elastic spring network preserves the biconcave shape of the RBC in the sense that after the removal of the body force for driving the Poiseuille flow, the RBC with its typical parachute shape in a tube does restore its biconcave resting shape. As a benchmark test, the relationship between the deformation index and the capillary number of the RBCs flowing through a narrow cylindrical tube has been validated. For the migration properties of a single cell in a slit Poiseuille flow, a slipper shape accompanied by a cell membrane tank‐treading motion is obtained for Re , and the cell mass center is away from the center line of the channel due to its asymmetric slipper shape. For the lower Re ?0.0137, an RBC with almost undeformed biconcave shape has a tumbling motion. A transition from tumbling to tank‐treading happens at the Reynolds number between 0.0137 and 0.03. In slit Poiseuille flow, the RBC can also exhibit a rolling motion like a wheel during the migration when the cell is released in the fluid flow with φ = π/2 and θ = π/2 (see Figure 12 for the definition of φ and θ). The lower the Reynolds number, the longer the rolling motion lasts; but the equilibrium shape and position are independent from the cell initial position in the channel. Copyright © 2014 John Wiley & Sons, Ltd.     

A New Low-Reynolds-Number One-Equation Model of Turbulence

In this study, we propose a new Low-Reynolds-Number (LRN)one-equation model, which is derived from an LRN two-equation(k-ε) model. The derivation of the transport equation, in principle, is based on the assumption that the turbulent structure parameter remains constant. However, the relation for the turbulent structure parameter a ₁(=|− |/k) is modified to account for near-wall turbulence. As a result, the present one-equation model contains a term which takes the near-wall limiting behavior explicitly into account. Thus, the present model provides the correct wall-limiting behavior of turbulence in the vicinity of the wall and can be applied to the analysis of heat transfer. The validity of the present model is tested in channel flows, boundary layer flows with and without pressure gradient, plane wall jet, and flow with separation and reattachment. The calculated results showed good agreement with the direct numerical simulation (DNS) and experimental data. This revised version was published online in July 2006 with corrections to the Cover Date.     

Rotationally symmetric spontaneous swirling in MHD flows

The stability of steady axisymmetricMHD flows of an inviscid, incompressible, perfectly conducting fluid with respect to swirling—perturbations of the azimuthal components of the velocity field—is studied in a linear approximation. It is shown that for flows similar to a magnetohydrodynamic Hill-Shafranov vortex, the problem reduces to a one-dimensional problem on a closed streamline of the unperturbed flow (the arc length of the streamline is the spatial coordinate). A spectral boundary-value eigenvalue problem is formulated for a system of two ordinary differential equations with periodic coefficients and periodic boundary conditions. Sufficient conditions under which swirling is impossible are obtained. Numerical solution of the characteristic equation shows that, under certain conditions, for each streamline there is a real eigenvalue that yields monotonic exponential growth of the initial perturbations. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 120–129, September–October, 2000.     

Persistent Non-Homogeneous Features in Periodic Channel-Flow Simulations

Time-resolved simulations of simple shear flows, such as boundary layers and channel flows, are often used as precursor simulations that provide the inflow-boundary conditions for simulations of turbulent flows in and around more complex geometries. For both the precursor and main simulations, the accuracy of the calculated mean flow relies on the simulations being run for long enough to contain the full spectrum of turbulent processes, resulting in a physically valid statistical representation. The time scale needed to achieve convergence of statistics from fundamental studies of simple shear flows is based on data that is averaged in spatial directions in which the flow geometry is invariant—i.e. directions in which homogeneity is expected to be the limiting case. This paper reports and discusses features that represent significant departures from spatial homogeneity of the flow in such a direction, that persist on this time scale, thereby limiting the spatial uniformity of a simulated turbulent inflow. The persistence and size of the features is quantified. A range of simulations for different combinations of domain dimensions and flow parameters has been performed with two independent codes (DNS and LES) to explore how the persistence and size are controlled. While no definitive physical mechanism has been identified, it is suggested that the features may be related to experimental observations of persistent structures in wall-bounded flows.     

Influence of Reynolds number on characteristics of turbulent wall boundary layers

Hot-wire anemometer measurements, using two types of probes, are reported for wall boundary layer flows with particular attention being given to the near-wall region and to measurements at high Reynolds numbers up to R 15,000. To obtain accurate near-wall measurements, the influence of wall proximity on hot-wire readings was eliminated by using a highly insulating wall material. Measurements were carried out with a single hot-wire boundary layer probe to obtain the longitudinal velocity informatemperature-wake sensor for the cross flow tion and a hot-wire, information.The results provided in the paper include measurements of averaged properties like mean velocity, rms-quantities of velocity fluctuations, probability density distributions etc. Conditional averages are also provided in order to yield information related to coherent flow structures present in boundary layer flows. It is shown that these structure remain present up to the highest Reynolds number investigated in the present study. The conditionally averaged data provide quantitative information on the mechanisms that are involved in the production of turbulence in boundary-layer flows.     

Extended proper orthogonal decomposition: a tool to analyse correlated events in turbulent flows

A tool to analyse correlated events in turbulent flows based on an extended proper orthogonal decomposition (POD) is proposed in this paper. A general definition of extended POD modes is presented and their properties are demonstrated. If the initial POD analysis in a spatio-temporal domain S concerns, for example, velocity—the concept of extended modes can be applied to study the correlation of any physical quantity in any domain with the projection of the velocity field on POD modes in S. The link with particular associations of POD and linear stochastic estimation (LSE) recently proposed is demonstrated at the end of the paper. The method is believed to provide a valuable tool to extend the well-documented POD analysis of eddy structures in turbulent flows, for example, in boundary layers or free shear flows. If extended modes are velocity modes, spatial and temporal interactions between eddy structures can be detected and studied. The rapid development of experimental diagnostic techniques now permit measurements of the concentration in the domain, the velocity of a dispersed phase in the domain or the static pressure at the boundary together with the fluid velocity field. Using this method we are then able to extract objectively the link between the representative groups of velocity modes and the correlated part of the concentration, particle motion or pressure signals.     

A vorticity stretching diagnostic for turbulent and transitional flows

Vorticity stretching in wall-bounded turbulent and transitional flows has been investigated by means of a new diagnostic measure, denoted by Γ, designed to pick up regions with large amounts of vorticity stretching. It is based on the maximum vorticity stretching component in every spatial point, thus yielding a three-dimensional scalar field. The measure was applied in four different flows with increasing complexity: (a) the near-wall cycle in an asymptotic suction boundary layer (ASBL), (b) K-type transition in a plane channel flow, (c) fully turbulent channel flow at Re _τ = 180 and (d) a complex turbulent three-dimensional separated flow. Instantaneous data show that the coherent structures associated with intense vorticity stretching in all four cases have the shape of flat ‘pancake’ structures in the vicinity of high-speed streaks, here denoted ‘h-type’ events. The other event found is of ‘l-type’, present on top of an unstable low-speed streak. These events (l-type) are further thought to be associated with the exponential growth of streamwise vorticity in the turbulent near-wall cycle. It was found that the largest occurrence of vorticity stretching in the fully turbulent wall-bounded flows is present at a wall-normal distance of y ⁺?=?6.5, i.e. in the transition between the viscous sublayer and buffer layer. The associated structures have a streamwise length of ~200–300 wall units. In K-type transition, the Γ-measure accurately locates the regions of interest, in particular the formation of high-speed streaks near the wall (h-type) and the appearance of the hairpin vortex (l-type). In the turbulent separated flow, the structures containing large amounts of vorticity stretching increase in size and magnitude in the shear layer upstream of the separation bubble but vanish in the backflow region itself. Overall, the measure proved to be useful in showing growing instabilities before they develop into structures, highlighting the mechanisms creating high shear region on a wall and showing turbulence creation associated with instantaneous separations.     

A turbulent boundary layer over a two-dimensional rough wall

Particle image velocimetry (PIV) measurements and planar laser induced fluorescence (PLIF) visualizations have been made in a turbulent boundary layer over a rough wall. The wall roughness consisted of square bars placed transversely to the flow at a pitch to height ratio of λ/k = 11 for the PLIF experiments and λ/k = 8 and 16 for the PIV measurements. The ratio between the boundary layer thickness and the roughness height k/δ was about 20 for the PLIF and 38 for the PIV. Both the PLIF and PIV data showed that the near-wall region of the flow was populated by unstable quasi-coherent structures which could be associated to shear layers originating at the trailing edge of the roughness elements. The streamwise mean velocity profile presented a downward shift which varied marginally between the two cases of λ/k, in agreement with previous measurements and DNS results. The data indicated that the Reynolds stresses normalized by the wall units are higher for the case λ/k = 16 than those for λ/k = 8 in the outer region of the flow, suggesting that the roughness density effects could be felt well beyond the near-wall region of the flow. As expected the roughness disturbed dramatically the sublayer which in turn altered the turbulence production mechanism. The turbulence production is maximum at a distance of about 0.5k above the roughness elements. When normalized by the wall units, the turbulence production is found to be smaller than that of a smooth wall. It is argued that the production of turbulence is correlated with the form drag.